Strong orbit equivalence in Cantor dynamics and simple locally finite groups
Volume 260 / 2023
Fundamenta Mathematicae 260 (2023), 1-20
MSC: Primary 37B02; Secondary 03E15.
DOI: 10.4064/fm227-7-2022
Published online: 3 November 2022
Abstract
We study certain countable locally finite groups attached to minimal homeomorphisms, and prove that the isomorphism relation on simple, countable, locally finite groups is a universal relation arising from a Borel $S_\infty $-action. This work also provides a dynamical approach to a result of Giordano, Putnam and Skau characterizing strong orbit equivalence.
